On Quantum Algorithms for Noncommutative Hidden Subgroups
Mark Ettinger, Peter Hoyer
Abstract
Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden subgroups of noncommutative groups. We present a quantum algorithm for the special case of dihedral groups which determines the hidden subgroup in a linear number of calls to the input function. We also explore the difficulties of developing an algorithm to process the data to explicitly calculate a generating set for the subgroup. A general framework for the noncommutative hidden subgroup problem is discussed and we indicate future research directions.
Create a lesson
Related papers
Approximate Synthetic Spectra of Quantum Systems Associated with Compact Lie Groups
Junyang Liu, Hang Wang, Houjin Wang et al.
An example of universal braiding in Links--Gould topological quantum computation
Matthew Harper, Ben-Michael Kohli
Reasoning about Shared-Qubit Concurrency in Quantum Computing
Mingsheng Ying
Information-Geometric Representation of Upper Bounds on Fluctuation Growth in Open Quantum Systems
Newshaw Bahreyni, Paul M. Alsing
Initialization-controlled fault sensitivity and force-balance plateaus in noisy variational quantum optimization
Longhui Shen, Fangzhou Jin, Bin Guo
Quantum identity authentication protocol via perturbed probability amplitudes
Xiangqun Fu, Zheng Han, Hongwei Li et al.